Paradoxes: Between Revision and Accommodation

With the rise of paraconsistent logics, contradictions need no longer be seen as a threat to rationality: one may embrace them, without going trivial. This, however, brings a methodological challenge when one is facing a paradox. Broadly speaking, paradoxes are derivations leading from the plausible to the implausible; when the conclusion is a contradiction, the implausible is an explicit contradiction. Now, with paraconsistent logics, such implausibility need no longer be seen as logically trivializing. As a result, the paradox may be embraced as plausible reasoning, with the contradiction accommodated in our overall system. This conflicts with more traditional approaches, requiring that contradictions be eliminated by revision of the derivation. Given that now two paths are available, do we have any reason to prefer one option over the other? In this paper, we argue that the accommodation camp faces difficulties when a form of methodological naturalism is embraced.